In certain exceptional cases, the airlines will allow nonrefundable tickets to be refunded if you need to cancel your plans because of the illness or death of your traveling companion or a close relative. Usually, you are urged at the time of purchase to take out travel insurance to cover this contingency. Sometimes charging a ticket on a credit card will give you some travel cancellation insurance.
An airline may offer a discounted fare (sometimes a minor discount, sometimes a generous discount) when a close relative becomes seriously ill or dies, causing you to travel without any advance planning. Who must be ill or have died for you to obtain a bereavement fare varies among airlines. For example, some airlines will give a discounted fare to attend the funeral of a parent, child, sibling, spouse, or in-laws only, while other airlines include non-marital partners and their immediate family members.
However, policies vary, as well as circumstances. If you are going to a memorial service scheduled for next week, even for your immediate relative, the airline will probably not offer you a bereavement discount.